Tamil Nadu 11th Std Model Question Paper Statistics

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3469 (NS)
!3469NSIstYearStatistics! £vÄ Gs
Register Number

PART - III
¦Òΰ¯À / STATISTICS
( uªÌ ©ØÖ® B[Q» ÁÈ / Tamil & English Version )

Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 70
Time Allowed : 3.00 Hours ] [Maximum Marks : 70

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP £vÁõQ EÒÍuõ GߣuøÚ
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU
PsPõo¨£õÍ›h® EhÚi¯õPz öu›ÂUPÄ®.
(2) }»® AÀ»x P¸¨¦ ø©°øÚ ©mk÷© GÊxÁuØS®
AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
ö£ß]À £¯ß£kzuÄ®.

Instructions : (1) Check the question paper for fairness of printing. If there is any lack of
fairness, inform the Hall Supervisor immediately.
(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.

£Sv & I / PART – I

SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 15x1=15

(ii) öPõkUP¨£mkÒÍ ©õØÖ ÂøhPÎÀ ªPÄ® Hئøh¯
Âøhø¯z ÷uº¢öukzxU SÔ±mkhß Âøh°øÚ²® ÷\ºzx
GÊuÄ®.
Note : (i) Answer all the questions.

(ii) Choose the most appropriate answer from the given four alternatives and
write the option code and the corresponding answer.

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3469 (NS) 2

1. ©¸zxÁ©øÚ°À C¸¢u ÷|µzvÀ J¸ ÷|õ¯õ롧 öÁ¨£{ø» 1008F
Gߣx :

(A) ÂQu AÍÄ (B) £s¦ AÍÄ

(C) Á›ø\ AÍÄ (D) CøhöÁÎ AÍÄ

The temperature of a patient during hospitalization is 1008F, is in :

(a) Ratio scale (b) Nominal scale

(c) Ordinal scale (d) Interval scale

2. J¸ ©õv›°À EÒÍ A»SPÎß GsoUøP ________ GÚ¨£k®.

(A) Gs AÍÄ (B) ©õv› AÍÄ

(C) •Êø©z öuõSv°ß AÍÄ (D) £s¦ AÍÄ
The number of units in the sample is called __________.

(a) Numerical measure (b) Sample size

(c) Population size (d) Nominal scale

3. B´Áõͺ J¸ {ÖÁÚzvß uµÂøÚ¨ £¯ß£kzxQÓõº GÛÀ,
AzuµÁõÚx :

(A) •uÀ {ø» uµÄ (B) Gs AÍ»õÚ uµÄ

(C) £s£Í»õÚ uµÄ (D) Cµshõ® {ø» uµÄ
When the researcher uses the data of an agency, then the data is called :

(a) Primary data (b) Quantitative data

(c) Qualitative data (d) Secondary data

3 3469 (NS)

4. usk & Cø»¨ £vÄ •øÓ°À SÔ¨¤h¨£k® usk¨ £Sv°À Ch®
ö£Ö® C»UP® :
(A) |k C»UP® (B) •ß C»UP®
(C) ¤ß C»UP® (D) C»UP®
In a stem and leaf plot, stem is the label for __________ digit.
(a) middle (b) leading
(c) trailing (d) digit

5. G¢u ÂÍUP¨£hzvÀ uµÄPÒ ÷Põn[PÍõP ©õØÓ¨£kQÓx ?
(A) £µÁÀ ö\ÆÁP¨ £h® (B) E¸Á ÂÍUP¨£h®
(C) ö£›m÷hõ Áøµ£h® (D) Ámh ÂÍUP¨£h®
In which diagram, data is transformed into angles ?
(a) Histogram (b) Pictogram
(c) Pareto diagram (d) Pie diagram

6. G¢u \uÂQu ©v¨¦ 5&Áx ©ØÖ® 25&Áx ¡ØÖ©õÚ[PÐUS Cøh°À
Aø©²® ?
(A) 20% (B) 15% (C) 30% (D) 75%
What percentage of values lies between 5th and 25th percentile ?
(a) 20% (b) 15% (c) 30% (d) 75%

7. J¸ {PÌöÁs £µÁ¼À •Pk Gߣx :
(A) |k ©v¨¦ (B) ]Ö© {PÌöÁs
(C) ö£¸© {PÌöÁs (D) {PÌöÁs
Mode is that value in a frequency distribution which possesses :
(a) Middle value (b) Minimum frequency
(c) Maximum frequency (d) Frequency

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3469 (NS) 4

8. Ch¨£UP •øÚ }sk EÒÍ ÁøÍÁøµ ________ BS®.
(A) ÷|›øhU ÷Põmh® (B) \©a^º
(C) Gv›øhU ÷Põmh® (D) ÷©ØTÔ¯ AøÚzx®
When referring to a curve, excess tail to the left end, you would call it :

(a) Positively skewed (b) Symmetrical

(c) Negatively skewed (d) All of these

9. 50 ©v¨¦PÎß vmh»UP® 8. JÆöÁõ¸ ©v¨ø£²® 2&BÀ ö£¸UQÚõÀ
QøhUS® ©v¨¦PÎß vmh»UP©õÚx :
(A) 8 (B) 4 (C) 2 (D) 16
The standard deviation of a set of 50 observations is 8. If each observation is multiplied
by 2, then the new value of standard deviation will be :

(a) 8 (b) 4 (c) 2 (d) 16

10. x10&ß ÁøPUöPÊ :

(A) 10x 9 (B) x10 (C) x 9 (D) 9x 9
Derivative of x10 is :

(a) 10x 9 (b) x 10 (c) x9 (d) 9x 9

11. Pou {PÌuPÄ ¤ßÁ¸©õÖ AøÇUP¨£kQÓx ?
(A) ¤¢øu¯ {PÌuPÄ (B) ¦Òΰ¯À {PÌuPÄ
(C) £õµ®£›¯ {PÌuPÄ (D) AÝ£Á {PÌuPÄ
Mathematical probability may also be termed as :

(a) Posteriori probability (b) Statistical probability

(c) Classical probability (d) Empirical probability

5 3469 (NS)

12. J¸ ÁõµzvÀ v[PmQÇø© Á¸ÁuØPõÚ {PÌuPÄ __________.

1 1 2
(A) 0 (B) 4 (C) 7 (D) 7

Probability of getting a Monday in a week is __________.

1 1 2
(a) 0 (b) (c) (d)
4 7 7

13. F(x) Gߣx J¸ £µÁÀ \õº£õÚõÀ F(−∞) Gߣx __________.

1 1
(A) 4 (B) 0 (C) 1 (D) 2

If F(x) is a distribution function, then F(−∞) is :

1 1
(a) (b) 0 (c) 1 (d)
4 2

14. B(n, p) &Cß \µõ\› ©ØÖ® ©õÖ£õk •øÓ÷¯ :

(A) npq , np (B) npq, np (C) np, npq (D) np, npq

The mean and variance of B(n, p) are :

(a) npq , np (b) npq, np (c) np, npq (d) np, npq

15. ________ J¸ vmh C¯À{ø»¨ £µÁø»U SÔUQÓx.

(A) N(µ, σ) (B) N(µ, σ2) (C) N(0, 1) (D) N(1, 0)
__________ represents a Standard Normal distribution.

(a) N(µ, σ) (b) N(µ, σ2) (c) N(0, 1) (d) N(1, 0)

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3469 (NS) 6

£Sv & II / PART – II

SÔ¨¦ : GøÁ÷¯Ý® BÖ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 24 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 6x2=12

Note : Answer any six questions. Question Number 24 is compulsory.

16. •Êø©z öuõSvø¯ Áøµ¯ÖUPÄ®.

Define population.

17. Á›ø\ Gߣx GßÚ?

What is an array ?

18. TÖ£møh ÂÍUP¨£hzøu ÂÍUSP.

Explain Component Bar diagram.

19. J¸ ÁS¨¤À 4 ©õnÁºPЮ, 3 ©õnÂPЮ EÒÍÚº. ©õnÁºPÒ ©ØÖ®
©õnÂPÎß \µõ\› ©v¨ö£sPÒ •øÓ÷¯ 20 ©ØÖ® 30 GÛÀ, A¢u
ÁS¨¤ß \µõ\› ©v¨ö£sønU PõsP.

A class consists of 4 boys and 3 girls. The average marks obtained by the boys and girls
are 20 and 30 respectively. Find the class average.

20. Q1=40, Q2=50, Q3=60 GÛÀ, ö£Í¼°ß ÷PõmhUöPÊ PõsP.

If Q1=40, Q2=50, Q3=60, find Bowley’s co-efficient of skewness.

7 3469 (NS)

21. Q›UöPm AoUPõP 13 Âøͯõmk õºPÐÒ 11 õºPøÍU öPõsh J¸
SÊ öu›Ä ö\´¯¨£h C¸UQÓx. Cøu GzuøÚ ÁÈPÎÀ öu›Ä
ö\´¯»õ®?
Out of 13 players, 11 players are to be selected for a cricket team. In how many ways
can this be done ?

22. J¸ £õ´éõß £µÁ¾US C¸ GkzxUPõmkPÒ u¸P.
Give any two examples of a Poisson distribution.

23. f (x)=5x4, 0 < x < 1 Gߣx J¸ {PÌuPÄ Ahºzva \õº£õS©õ?

Verify whether f (x)=5x4, 0 < x < 1 is a p.d.f.

24. C¸ £PøhPÒ Ã_®÷£õx TkuÀ 11 Qøh¨£uØPõÚ {PÌuPÄ ¯õx ?
When two dice are thrown, what is the probability of getting a sum 11 ?

£Sv & III / PART – III

SÔ¨¦ : GøÁ÷¯Ý® BÖ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 33 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 6x3=18

Note : Answer any six questions. Question Number 33 is compulsory.

25. QµõUìhß ©ØÖ® öPÍhß AÁºPÎß ¦Òΰ¯À Áøµ¯øÓø¯ GÊxP.
Discuss the definition of Statistics according to Croxdon and Cowden.

26. £Û£¢x ©õv›U Po¨¦ •øÓ Gߣøu ÂÁ›UPÄ®.
Explain the method of snowball sampling.

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3469 (NS) 8

27. J¸ {ÖÁÚ® u¯õ›zu ö£õ¸mPÎß EØ£zv Âø» (` C»m\[PÎÀ) R÷Ç
öPõkUP¨£mkÒÍx.
Bsk EØ£zv Âø»
2010 55
2011 40
2012 30
2013 25
2014 35
2015 70
Gί £møh ÂÍUP¨£h® ÁøµP.
The production cost of the company in lakhs of rupees is given below.
Year Production cost
2010 55
2011 40
2012 30
2013 25
2014 35
2015 70
Construct a simple bar diagram.

28. R÷Ç öPõkUP¨£mkÒÍ uµÂØS P60 PõsP.
x 06 09 12 15 18
f 7 12 19 10 2
Evaluate P60 from the following data.
x 06 09 12 15 18
f 7 12 19 10 2

29. 7 öÁÆ÷ÁÖ |õmPÎÀ J¸ £ÒΰÀ ¡»Pzv¼¸¢x öPõkUP¨£mh
¦zuP[PÎß GsoUøP 7, 9, 12, 15, 5, 4, 11. ¦zuP[PÎß GsoUøPPÎß
vmh»UP® PõsP.
The following data gives the number of books taken by a school library in 7 days.
7, 9, 12, 15, 5, 4, 11. Find the standard deviation of the books taken.

9 3469 (NS)

1
30. ∫ 2x dx &ß ©v¨¦ PõsP.
−1

1
Evaluate : ∫ 2 x dx .
−1

31. |ßS Pø»UP¨£mh 52 ^mkPÒ öPõsh ^mk Pmi¼¸¢x J¸ ^mk
÷uº¢öukUP¨£kQÓx. Ax (i) J¸ Hì (ii) J¸ øh©sm ^mhõP C¸UP
{PÌuPÄ PõsP.
A card is drawn at random from a well shuffled pack of 52 cards. What is the probability
that it is (i) an ace (ii) a diamond card ?

32. J¸ £õ´\õß £µÁ¼À 3P(X=2)=P(X=4) GÛÀ, λ&Cß ©v¨ø£U PõsP.
In a Poisson distribution, 3P(X=2)=P(X=4). Find its parameter λ.

33. J¸ \©Áõ´¨¦ ©õÔ X ¤ßÁ¸® {PÌuPĨ £µÁø»¨ ö£ØÔ¸UQÓx.
X=x 5 2 1

1 1 1
P(x)
4 2 4

X- ß Gvº£õºzuø»U PõsP.

A random variable X has the following probability distribution.

X=x 5 2 1

1 1 1
P(x)
4 2 4

Find the expected value of X.

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3469 (NS) 10

£Sv & IV / PART – IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 5x5=25
Note : Answer all the questions.

34. (A) P.C. ©í»÷Úõ¤ì AÁºPÎß £[PΨø£¨ £ØÔ J¸ SÔ¨¦ ÁøµP.
AÀ»x
(B) R÷Ç öPõkUP¨£mh uµÂØS RÈÚ SÂÄ {PÌöÁs ÁøÍ÷Põk
ÁøµP.

vÚUT¼ (`) 70-80 80-90 90-100 100-110 110-120 120-130 130-140 140-150

÷Áø»¯õmPÎß
12 18 35 42 50 45 20 8
GsoUøP
(a) Write a brief note on the contributions by P.C. Mahalonobis.
OR
(b) Draw the less than Ogive curve for the following data.

Daily wages (in ` ) 70-80 80-90 90-100 100-110 110-120 120-130 130-140 140-150
No. of workers 12 18 35 42 50 45 20 8

35. (A) ÂÚõ¨£mi¯À u¯õ›zu¼À EÒÍ ÁÈPõmkuÀPÒ GßÚ? ÷©¾®
AÁØøÓ¨ £ØÔ ÂÁ›UPÄ®.
AÀ»x
(B) \µõ\› ©ØÖ® Cøh{ø» AÍÄ PõsP.
T¼ (`) 60-70 50-60 40-50 30-40 20-30
öuõÈ»õͺPÎß 5 10 20 5 3
GsoUøP
(a) What are the guiding considerations in the construction of a questionnaire ?
Explain.
OR
(b) Find the Mean and Median.
Wages (`) 60-70 50-60 40-50 30-40 20-30
No. of labourers 5 10 20 5 3

11 3469 (NS)

36. (A) RÌPsh uµÄPÐUS PõÀ©õÚ Â»UP® PnUQkP.

AÍÄ 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40

{PÌöÁs 6 10 18 30 15 12 10 6 2

AÀ»x
(B) ¤øǯØÓ Gmk |õn¯[PÒ J÷µ \©¯zvÀ _sh¨£kQßÓÚ GÛÀ,
SøÓ¢ux BÖ uø»PÒ Qøh¨£uØPõÚ {PÌuPøÁU PõsP.
(a) Compute Quartile deviation from the following data.

Size 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40
Frequency 6 10 18 30 15 12 10 6 2

OR

(b) Eight coins are tossed simultaneously. Find the probability of getting at least six
heads.

37. (A) ÁøP¨£kzxu¼ß £À÷ÁÖ ÁøPPøÍ ÂÍUSP.
AÀ»x
(B) J¸ ÂÚõzuõÎÀ A ¤›ÂÀ 5 ÂÚõUPЮ, B ¤›ÂÀ 7 ÂÚõUPЮ
EÒÍÚ. J¸ ©õnÁß C¸ ¤›ÄPξ® SøÓ¢u£m\® 3 ÂÚõUPøÍz
öu›Ä ö\´x ö©õzu® 8 ÂÚõUPÐUS Âøhuµ ÷Áskö©ÛÀ,
GzuøÚ ÁÈPÎÀ ÂÚõUPøÍz öu›Ä ö\´¯»õ®?
(a) Explain various types of classification.

OR

(b) A question paper contains section A with 5 questions and section B with
7 questions. A student is required to attempt 8 questions in all, selecting at least
3 from each section. In how many ways can a student select the questions ?

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3469 (NS) 12

38. (A) J¸ ö£mi°À 3 ]Á¨¦ ©ØÖ® 4 }» {Ó PõÀ EøÓPÒ (socks) EÒÍÚ.
Cµsk PõÀ EøÓPøÍ J÷µ {ÓzvÀ ÷uº¢öuk¨£uØPõÚ {PÌuPÄ
PõsP.
AÀ»x
(B) J¸ £Pøh E¸mh¨£kQÓx. A¨£Pøh°À ÷uõßÖ® Gs X GÛÀ,
E(X), E(X2) ©ØÖ® ©õÖ (X) PõsP.

(a) A box contains 3 red and 4 blue socks. Find the probability of choosing two socks
of the same colour.

OR

(b) When a die is thrown, X denotes the number turning up. Find E(X), E(X2) and
Var(X).

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